In this section, we briefly review Poincaré symmetry in the context of celestial amplitudes, studied for example in [1]}. The Lorentz subgroup of Poincaré in four dimensions is realized by the global conformal group in two dimensions. As familiar from 2D CFT, the generators \(L_n\) , \({\bar{L}}_n\) , \(n= 0, \pm 1\)  respect
\(\begin{split}\left[L_m, L_n\right] = (m-n)L_{m+n}, \quad \quad \quad \left[\bar{L}_m, \bar{L}_n\right] = (m-n)\bar{L}_{m+n},\end{split}\) 
